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Here is an 'aide memoire'.
SOH, CAH, TOA.
Expanding this aide.
SOH ; is Sine , Oppositre, and Hypotenuse.
CAH ; is Cosibe, Adjacent and Hypotenuse.
TOA ; is Tangent, Opposite and Adjacent.
To put these in algenraic format .
Sine(angle) = opposite / hypotenuse
Cosine(angle) = adjcent / hypotenuse
Tangent(angle) = opposite/ adjacent.
And in algenraic short-hand format.
Sin(angle) = O/H
Cos(angle) = A/H
Tan(angle) = O/A
For any given Right-angled triangle, the Hypotenuse is always the side opposite to the right angle.
Taking one of the other anglers. Then the Opposite is the side length oppisite to the given angle. Then the Adjacent is the side length to the given angle.
NB Taking the third angle, then the opposite(O) and the adjacent(A) ' swop places.
The above three equations can all be algebraically rearranged. 'Sine' is shown, bit the other two can also be rearranged.
Sin(angle) = O/H
H X Sin(angle) = O
[Sin(angle)] / O = H
Angle = Sin(-1) [O/H] or ArcSin [O/H].
An example
A right angled triangle of hypotenuse '2'. and an angle of 30 degrees.
Then
Sin(30) = O/2
On your calculator ; Sin(30) = 1/2 or 0.5
Substituting.
1/2 = O / 2
Algebraically rearrange
O = 2 X 1/2 = 2/2 = 1/1 = 1
So the opposite side is equal to '1'.
Correspondingly
Sin(angle) = O/H = 1/2
Then
Angle = Sin^(-1)[1/2]
On your calculator, using the 'inverse/arcsin' button of Sin
Then
angle = 30 degrees.
These work for any Trig. Functions. However, for any given value of an angle, you will have some 'horrible' decimal number.
Sin(79) = 0.98167183.... usuallu shortened to 4 d.p. at 0.9817. or 6 d.p. 0.981672
Hope that helps!!!!!
What else can I help you with?
How do you find the hypotenuse of a right triangle when only a side length and angle is given?
Dependent on what side you are given you would use Sin(Θ) = Opposite/Hypotenuse just rearrange the formula to Hypotenuse = Opposite/Sin(Θ). Or if you are given the adjacent side use Cosine(Θ)=Adjacent/Hypotenuse, then: Hypotenuse = Adjacent/Cosine(Θ)
What are the Names of all trigonometry functions?
The basic functions are sine, cosine, tangent, cosecant, secant and cotangent. In addition, there are their inverses, whose full names use the prefix "arc" [arcsine, arc cosine, etc] but are more often written as sin-1, cos-1 and so on.
How do you solve COS?
To solve for the cosine (COS) of an angle, you can use the unit circle, where the cosine of an angle corresponds to the x-coordinate of the point on the circle at that angle. Alternatively, you can use trigonometric identities or the cosine function on a scientific calculator by inputting the angle in degrees or radians. For specific problem solving, using the cosine rule in triangles may also be applicable to find unknown sides or angles.
How do you solve double angle equations for trigonometry?
There are two ways to solve for the double angle formulas in trigonometry. The first is to use the angle addition formulas for sine and cosine. * sin(a + b) = sin(a)cos(b) + cos(a)sin(b) * cos(a + b) = cos(a)cos(b) - sin(a)sin(b) if a = b, then * sin(2a) = sin(a)cos(a) + cos(a)sin(a) = 2sin(a)cos(a) * cos(2a) = cos2(a) - sin2(b) The cooler way to solve for the double angle formulas is to use Euler's identity. eix = cos(x) + i*sin(x). Yes, that is "i" as in imaginary number. we we put 2x in for x, we get * e2ix = cos(2x) + i*sin(2x) This is the same as * (eix)2 = cos(2x) + i*sin(2x) We can substitute our original equation back in for eix. * (cos(x) + i*sin(x))2 = cos(2x) + i*sin(2x) We can distribute the squared term. * cos2(x) + i*sin(x)cos(x) + i*sin(x)cos(x) + (i*sin(x))2 = cos(2x) + i*sin(2x) And simplify. Because i is SQRT(-1), the i squared term becomes negative. * cos2(x) + 2i*sin(x)cos(x) - sin2(x) = cos(2x) + i*sin(2x) * cos2(x) - sin2(x) + 2i*sin(x)cos(x) = cos(2x) + i*sin(2x) Now you can plainly see both formulas in the equation arranged quite nicely. I don't yet know how to get rid of the i, but I'm working on it.
How do you calculate sin20?
Sin(20) = You need either a scientific calculator or Castles four figure Tables. Using a scientific calculator Sin ( 20 ) = 0.342020143.... Sin(20) ~ 0.3420 (4d.p.).
How do you know when to use sine over cosine or cosine over sine?
You can choose either or but tangent which is sin/cos seems to be the most common way.
How do you find the hypotenuse of a right triangle when only a side length and angle is given?
Dependent on what side you are given you would use Sin(Θ) = Opposite/Hypotenuse just rearrange the formula to Hypotenuse = Opposite/Sin(Θ). Or if you are given the adjacent side use Cosine(Θ)=Adjacent/Hypotenuse, then: Hypotenuse = Adjacent/Cosine(Θ)
How do you find out the top angle of an Isosceles triangle if you do not know the base angle?
It depends on whether you know the lengths of all three sides (either explicitly or otherwise). If you don't know the lengths of the sides you cannot find the top angle. If you do know the sides you can apply the cosine rule: cos(A) = (b2 +c2 - a2)/2bc and then use the inverse cosine function to determine A.
When do i use negative sin cos or tan?
The inverse (negatives) of sine, cosine, and tangent are used to calculate the angle theta (or whatever you choose to name it). Initially it is taught that opposite over hypotenuse is equal to the sine of theta sin(theta) = opposite/hypotenuse So it can be said that theta = sin-1 (opp/hyp) This works the same way with cosine and tangent In short the inverse is simply what you use when you move the sin, cos, or tan to the other side of the equation generally to find the angle
How do you find 2 missing sides of a right triangle?
Two methods to try . #1 Use pythagoras h^ = a^2 + a^2 NB THis is only good if you know that the two unknown sides are the same length. #2 Use trigonometry (trig.) This is good if you know the hypotenuse and one of the angles. Sine(angle) = opposite/ hypotenuse Hence opposite side = hypotenuse X sine(angle) Similarly Cosine(angle) = adjacent / hypotenuse. adjacent side = hypotenuse X Cosine(angle) Here is an example If you known the hypotenuse is a length of '6' and the angle is 30 degrees. Then opposite = 6 X Sin(30) opposite = 6 x 0.5 = 3 So the length of the oppisute sides is '3' units. NB DO NOT make the mistakes of saying Sin(6 X 30) = Sin(180) Nor 6 x 30 , nor Sin(6) X 30 , nor any other combination. You MUST find the SINE of the angle , then multiply it to the given length. Similarly for Cosine and Tangent.
If the exponent is in cosine the formula to use is cosine derivatives?
pen0r
When to use sin and cos.?
The sine and cosine were originally developed for use in surveying. They provided a way to measure the distance across lakes and around mountains. Soon they were found to be useful in navigation. The sine was used to calculate pi. When electrical measurements were made, the sine law was used. If you want to know when to use the sine and when to use the cosine, you will need to get a trig book, a physics book, an astronomy book, a sailing book, and a few other books and read them all.
What is the area of a triangle that has sides of 9cm 12cm and 14cm?
53.5 square cm to 1 d.p. Use the cosine rule to find an angle. Then use: Area = 1/2*a*b*sin C
Why we use sin cos etc in sinusoidal wave?
By its very mane, a sinusoidal wave refers to a sine function. The cosine function is simply the sine function that is phase-shifted.
How do you find a measurement of an angle in a triangle when you only know the side length?
If you do not know only a side length you cannot. If you know all three side lengths then you can use the cosine rule. You can continue using the cosine rule for the other two angles but, once you have one angle, it is simpler to use the sine rule.
How do you use cosine?
cosine = adjacent/hypotenuse. It can be used as other trig functions can.
What are the Names of all trigonometry functions?
The basic functions are sine, cosine, tangent, cosecant, secant and cotangent. In addition, there are their inverses, whose full names use the prefix "arc" [arcsine, arc cosine, etc] but are more often written as sin-1, cos-1 and so on.
